It should be “was”. “would have” is used when we try to state something which one should do or I should have done,something contrast. “had” will be inappropriate because the buffalo is not supposed to wash it itself.

I think “has” is the right answer for this.
It seemed like this buffalo has never washed before I washed him this morning.
this sentence belongs to
“Past to present”
for that
have/has + v3 form is used.